Beyond the hype

Sequencing studies are increasingly being conducted to identify rare variants associated with complex traits. The limited power of classical single-marker association analysis for rare variants poses a central challenge in such studies. We propose the sequence kernel association test (SKAT), a supervised, flexible, computationally efficient regression method to test for association between genetic variants (common and rare) in a region and a continuous or dichotomous trait while easily adjusting for covariates. As a score-based variance-component test, SKAT can quickly calculate p values analytically by fitting the null model containing only the covariates, and so can easily be applied to genome-wide data. Using SKAT to analyze a genome-wide sequencing study of 1000 individuals, by segmenting the whole genome into 30 kb regions, requires only 7 hr on a laptop. Through analysis of simulated data across a wide range of practical scenarios and triglyceride data from the Dallas Heart Study, we show that SKAT can substantially outperform several alternative rare-variant association tests. We also provide analytic power and sample-size calculations to help design candidate-gene, whole-exome, and whole-genome sequence association studies.

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Rare-Variant Association Testing for Sequencing Data with the Sequence Kernel Association Test

Autism spectrum disorders (ASDs) represent a formidable challenge for psychiatry and neuroscience because of their high prevalence, lifelong nature, complexity and substantial heterogeneity. Facing these obstacles requires large-scale multidisciplinary efforts. Although the field of genetics has pioneered data sharing for these reasons, neuroimaging had not kept pace. In response, we introduce the Autism Brain Imaging Data Exchange (ABIDE)-a grassroots consortium aggregating and openly sharing 1112 existing resting-state functional magnetic resonance imaging (R-fMRI) data sets with corresponding structural MRI and phenotypic information from 539 individuals with ASDs and 573 age-matched typical controls (TCs; 7-64 years) (http://fcon_1000.projects.nitrc.org/indi/abide/). Here, we present this resource and demonstrate its suitability for advancing knowledge of ASD neurobiology based on analyses of 360 male subjects with ASDs and 403 male age-matched TCs. We focused on whole-brain intrinsic functional connectivity and also survey a range of voxel-wise measures of intrinsic functional brain architecture. Whole-brain analyses reconciled seemingly disparate themes of both hypo- and hyperconnectivity in the ASD literature; both were detected, although hypoconnectivity dominated, particularly for corticocortical and interhemispheric functional connectivity. Exploratory analyses using an array of regional metrics of intrinsic brain function converged on common loci of dysfunction in ASDs (mid- and posterior insula and posterior cingulate cortex), and highlighted less commonly explored regions such as the thalamus. The survey of the ABIDE R-fMRI data sets provides unprecedented demonstrations of both replication and novel discovery. By pooling multiple international data sets, ABIDE is expected to accelerate the pace of discovery setting the stage for the next generation of ASD studies.

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The autism brain imaging data exchange: towards a large-scale evaluation of the intrinsic brain architecture in autism

The usage of psychological networks that conceptualize behavior as a complex interplay of psychological and other components has gained increasing popularity in various research fields. While prior publications have tackled the topics of estimating and interpreting such networks, little work has been conducted to check how accurate (i.e., prone to sampling variation) networks are estimated, and how stable (i.e., interpretation remains similar with less observations) inferences from the network structure (such as centrality indices) are. In this tutorial paper, we aim to introduce the reader to this field and tackle the problem of accuracy under sampling variation. We first introduce the current state-of-the-art of network estimation. Second, we provide a rationale why researchers should investigate the accuracy of psychological networks. Third, we describe how bootstrap routines can be used to (A) assess the accuracy of estimated network connections, (B) investigate the stability of centrality indices, and (C) test whether network connections and centrality estimates for different variables differ from each other. We introduce two novel statistical methods: for (B) the correlation stability coefficient, and for (C) the bootstrapped difference test for edge-weights and centrality indices. We conducted and present simulation studies to assess the performance of both methods. Finally, we developed the free R-package bootnet that allows for estimating psychological networks in a generalized framework in addition to the proposed bootstrap methods. We showcase bootnet in a tutorial, accompanied by R syntax, in which we analyze a dataset of 359 women with posttraumatic stress disorder available online.

/pdf/estimating-psychological-networks-and-their-accuracy-a-ljt6ufq2za.pdf

Estimating Psychological Networks and their Accuracy : A tutorial paper

The cortical surface is organized into a large number of cortical areas; however, these areas have not been comprehensively mapped in the human. Abrupt transitions in resting-state functional connectivity (RSFC) patterns can noninvasively identify locations of putative borders between cortical areas (RSFC-boundary mapping; Cohen et al. 2008). Here we describe a technique for using RSFC-boundary maps to define parcels that represent putative cortical areas. These parcels had highly homogenous RSFC patterns, indicating that they contained one unique RSFC signal; furthermore, the parcels were much more homogenous than a null model matched for parcel size when tested in two separate datasets. Several alternative parcellation schemes were tested this way, and no other parcellation was as homogenous as or had as large a difference compared with its null model. The boundary map-derived parcellation contained parcels that overlapped with architectonic mapping of areas 17, 2, 3, and 4. These parcels had a network structure similar to the known network structure of the brain, and their connectivity patterns were reliable across individual subjects. These observations suggest that RSFC-boundary map-derived parcels provide information about the location and extent of human cortical areas. A parcellation generated using this method is available at http://www.nil.wustl.edu/labs/petersen/Resources.html.

/pdf/generation-and-evaluation-of-a-cortical-area-parcellation-3plntatxpn.pdf

Generation and Evaluation of a Cortical Area Parcellation from Resting-State Correlations

We propose a high dimensional semiparametric scale-invariant principle component analysis, named TCA, by utilize the natural connection between the elliptical distribution family and the principal component analysis. Elliptical distribution family includes many well-known multivariate distributions like multivariate Gaussian, t and logistic and it is extended to the meta-elliptical by Fang et.al (2002) using the copula techniques. In this paper we extend the meta-elliptical distribution family to a even larger family, called transelliptical. We prove that TCA can obtain a near-optimal s√log d/n estimation consistency rate in recovering the leading eigenvector of the latent generalized correlation matrix under the transelliptical distribution family, even if the distributions are very heavy-tailed, have infinite second moments, do not have densities and possess arbitrarily continuous marginal distributions. A feature selection result with explicit rate is also provided. TCA is further implemented in both numerical simulations and large-scale stock data to illustrate its empirical usefulness. Both theories and experiments confirm that TCA can achieve model flexibility, estimation accuracy and robustness at almost no cost.

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Transelliptical Component Analysis

Testing mutual independence for high-dimensional observations is a fundamental statistical challenge. Popular tests based on linear and simple rank correlations are known to be incapable of detecting nonlinear, nonmonotone relationships, calling for methods that can account for such dependences. To address this challenge, we propose a family of tests that are constructed using maxima of pairwise rank correlations that permit consistent assessment of pairwise independence. Built upon a newly developed Cramer-type moderate deviation theorem for degenerate U-statistics, our results cover a variety of rank correlations including Hoeffding’s D, Blum–Kiefer–Rosenblatt’s R and Bergsma–Dassios–Yanagimoto’s τ∗. The proposed tests are distribution-free in the class of multivariate distributions with continuous margins, implementable without the need for permutation, and are shown to be rate-optimal against sparse alternatives under the Gaussian copula model. As a by-product of the study, we reveal an identity between the aforementioned three rank correlation statistics, and hence make a step towards proving a conjecture of Bergsma and Dassios.

High-dimensional consistent independence testing with maxima of rank correlations

Rank correlations have found many innovative applications in the last decade. In particular, suitable versions of rank correlations have been used for consistent tests of independence between pairs of random variables. The use of ranks is especially appealing for continuous data as tests become distribution-free. However, the traditional concept of ranks relies on ordering data and is, thus, tied to univariate observations. As a result it has long remained unclear how one may construct distribution-free yet consistent tests of independence between multivariate random vectors. This is the problem we address in this paper, in which we lay out a general framework for designing dependence measures that give tests of multivariate independence that are not only consistent and distribution-free but which we also prove to be statistically efficient. Our framework leverages the recently introduced concept of center-outward ranks and signs, a multivariate generalization of traditional ranks, and adopts a common standard form for dependence measures that encompasses many popular measures from the literature. In a unified study, we derive a general asymptotic representation of center-outward test statistics under independence, extending to the multivariate setting the classical Hajek asymptotic representation results. This representation permits a direct calculation of limiting null distributions for the proposed test statistics. Moreover, it facilitates a local power analysis that provides strong support for the center-outward approach to multivariate ranks by establishing, for the first time, the rate-optimality of center-outward tests within families of Konijn alternatives.

Rate-optimality of consistent distribution-free tests of independence based on center-outward ranks and signs

We consider an increasingly popular study design where single-cell RNA-seq data are collected from multiple individuals and the question of interest is to find genes that are differentially expressed between two groups of individuals. Towards this end, we propose a statistical method named IDEAS (individual level differential expression analysis for scRNA-seq). For each gene, IDEAS summarizes its expression in each individual by a distribution and then assesses whether these individual-specific distributions are different between two groups of individuals. We apply IDEAS to assess gene expression differences of autism patients versus controls and COVID-19 patients with mild versus severe symptoms. 

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IDEAS: individual level differential expression analysis for single-cell RNA-seq data

This paper investigates the problem of testing independence of two random vectors of general dimensions. For this, we give for the first time a distribution-free consistent test. Our approach combines distance covariance with the center-outward ranks and signs developed in Hallin (2017). In technical terms, the proposed test is consistent and distribution-free in the family of multivariate distributions with nonvanishing (Lebesgue) probability densities. Exploiting the (degenerate) U-statistic structure of the distance covariance and the combinatorial nature of Hallin's center-outward ranks and signs, we are able to derive the limiting null distribution of our test statistic. The resulting asymptotic approximation is accurate already for moderate sample sizes and makes the test implementable without requiring permutation. The limiting distribution is derived via a more general result that gives a new type of combinatorial non-central limit theorem for double- and multiple-indexed permutation statistics.

Fang Han

Papers

Transelliptical Component Analysis

High-dimensional consistent independence testing with maxima of rank correlations

Rate-optimality of consistent distribution-free tests of independence based on center-outward ranks and signs

IDEAS: individual level differential expression analysis for single-cell RNA-seq data

Distribution-free consistent independence tests via center-outward ranks and signs